The Early Universe read chapter 13

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The Early Universeread chapter 13
We have discussed Models such as the Big Bang
and how the universe may have started from such
an explosive event The observable universe
today constrains the way things must have evolved
just after the Big Bang-so we can build a history
of the Early Universe
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Initially - size of universe was
smaller Assuming matterenergy is constant at
all epochs then of course the early universe had
much denser matter energy - hotter
temperature Difficult to determine what
conditions were -long before galaxies stars
formed, no sources which we can trace back that
far
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In the early universe the high density caused
elementary particles of all types to exchange
energy momentum Particles co-existed in an
equilibrium defined by temperaturemodels assume
early universe was in thermal equilibrium
-supported by the black-body shape of the CMB
spectrum
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Universe contains a mass density energy
density Present day- energy mostly CMB(CBR)
photons, gt 109 photons per matter
particle Photons lost energy as universe
expandednow energy density in CBR small compared
to matter densitythe universe today is matter
dominated Early universe had energy
dominating state of matter depended critically
on temperature Will examine temperature
matter evolution as a function of time
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Recall the Friedmann eqns Describe evolution
(into future) for scale factor based around
mass/density A soln, for a given k, ? is a model
of the universe Also, recall we found
so matter changes with 1/R2
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Friedmann Equation
Physical interpretation if there is more than a
certain amount of matter in the universe, the
attractive nature of gravity will ensure that the
Universe recollapses

• Scale factor as function of mass for future
  extrapolationbut how about backwards
  extrapolation, to a time when we had a high
  density of energy?

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The Friedmann Equations Photons carry energy
momentum - when they hit a particle they can
impart some of that momentum to it - so photons
exert a pressure For radiation-dominated era,
need to incorporate photon energy and thus
radiation pressure into Friedmann eqns, ie to
understand how scale factor must have evolved
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• The Friedmann Equations
• Need to relate energy-density scale factor
  R(t)
• Taking either eqn for local energy density and
  solving it OR
• following intuitive arguments like we used in
  last Tuesdays lecture
• it turns out
• ?(t)?(t1)R(t1)/ R(t)4
• , the energy density drops faster than just due
  to volume expansion of universe because cosmic
  redshift effects add in extra term
• Scaling with energy more dramatic than that with
  mass!

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The Friedmann Equations In thermal equilibrium
??T4 gives us temperature-scale relation T(t)
T(t1)R(t1)/ R(t) or T(tthen)
T(tnow)R(tnow)/ R(tthen) using our previous
relation gives T(tthen) T(tnow)(1
z) can measure temperature now and thus derive
temperature in the past versus redshift and thus
versus age or time after R(0).
now
then
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The Beginning of Time - Planck Epoch
T0s
T10-43 s
Planck epoch is t10 -43 sec
Think about the forces which dominate our life
today GRAVITY ELECTROMAGNETISM WEAK FORCE
STRONG FORCE Dominates Dominates
chemical Dominate atomic reactions at large
reactions distances
We believe during this time all 4 forces composed
a single force
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The Beginning of Time
T0s
T10-43 s
Gravity not yet incorporated into QM -need a
Theory of Everything Most of the time we can use
one or the other, depending on what size-scale we
are studying - as we consider t0, need both to
merge Theoretical models can (only) probe back
to 10-43 sec after the Big Bang, -called the
Planck time when the characteristic scale of the
universe was ct1.6x10-35m, the Planck length
Planck epoch is t10 -43 sec
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The Beginning of Time - Planck Epoch
T0s
T10-43 s
Planck epoch is t10 -43 sec At end of Planck
epoch gravitons fell out of equilibrium with the
other particles and gravity decoupled from the
other forces - first symmetry break
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Quantum field theory
Time Out
Waves ( hence allied particles) can be
associated with a field A field can be
mathematically represented as a quantity extended
in space/time -strengths of fields related to
of associated particles present Fields have
ripple-like fluctuations characterized by
wavelength ofn associated particle Gravity is the
field of the graviton (as-yet-undiscovered
particle) Most important are field symmetries,
quantities which are invariant under specific
transformations (think back to SR, or of things
like energy conservation laws) When conditions
change some symmetries stop we have spontaneous
symmetry breaking
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Quantum field theory
Time Out
When conditions change and some symmetries stop
we have spontaneous symmetry breaking Real life
analogytemperature changes cause phase
transitions like the melting of ice Water has
higher entropy and thus less symmetry than a
crystalline solid
o o o o o o o o o o o o o o o o o o o o o o o o
o o o o o o o o o o o o
o o o ooo o o o o o oo o o o o o
o o o o o o o o o o
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The Beginning of Time - Planck Epoch
T0-10-43 s
Planck epoch is t10-43 sec Recap At end
of Planck epoch gravitons fell out of equilibrium
with the other particles and gravity decoupled
from the other forces - first symmetry break
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Unified Epoch
t10 -43 sec --gt t10 -35 sec
Temperatures so high our understanding of matter
is minimal Grand Unified Theories (GUTs) exist
to try and describe the three unified forces
-theories incomplete
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Unified Epoch
t10 -43 sec --gt t10 -35 sec
These extreme conditions have not been reproduced
in an accelerator - lack of direct verification
means there are several GUT theories including
supersymmetry, superstrings and supergravity We
know current GUT models are not yet correct -
they underpredict the lifetime of the
proton Remnant of Unified Epoch is the excess
of matter over anti-matter, process which left
this is baryogenesis
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Pair Production
During this epoch sub-atomic particles crashed
together at relativistic speeds interacted with
photonsPhotons also collided created
particles (pair production) Threshold
temperature for specific particle creation -
temperature determines type of particles being
produced by pair production proton/anti-proton
production starts at T1013K T 2m0c2/3KB
Mean energy/particle ? temperature Higher
temperatures favor production of more massive
particles
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Matter/Anti-Matter
At this epoch pair production/annihilation rates
were in balance As universe expanded, cooled
the temperature dropped more types of particles
stopped being createdAt some point the symmetry
between matter/anti-matter must have been
violated Currently 1 particle of matter per 1
billion photons, thus the excess of matter over
anti-matter was 1 part in a billionThis slight
imbalance resulted in all that we can see
!!!Not yet a consensus as to why this is
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Quark Epoch
End of the UNIFIED EPOCH at t10 -35 sec -
temperatures dropped,- strong force decoupled and
we entered the Quark Epoch t10 -35 sec --gt t
10 -6 sec - the Quark Epoch universe consisted
of quarks other particles/anti-particles te
mperatures dropped to 1015K at t10-11 s -
decoupling occurred After decoupling, all forces
were separate - as they are today
QM predicts electromagnetic weak forces lose
separate identities at very high
temperatures/energies merge into a single
electroweak force Verified in particle
accelerators!!!
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Inflation - a period of great expansion of the
universe occurred during this epoch The
freezing-out of the strong force may have
liberated an enormous energy causing a period of
rapid expansion called inflation In as small a
time as 10-36s a piece of the universe the size
of an atomic nucleus grew to the size of our
solar system
inflation caused size change of field ripples
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Inflation lasted only a small amount of time, but
afterwards corners of the universe were widely
separated Before inflation AB could
equilibrate, inflation pushed them apart and now
we can see light from either, but light not yet
reached one from another
You can test inflation by comparing the amplitude
of the spatial irregularities in the CMB spectrum
with the predictions of inflation Right now its
looking pretty good
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The forces are distinct at low temperatures, but
appear to merge at high temperatures
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Hadron Epoch
T 10-6 - 10-4 s
After t 10-6 sec - quarks condensed into
hadrons (baryons mesons) Baryon/anti-baryon
pairs annihilated leaving photons, some unmatched
baryons then remained Excess matter has
survived with rest-mass intact
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Lepton Epoch
At t 10-4 sec - lighter particles associated
with the weak force (e.g. electrons, neutrinos
etc) gained domination, the lepton epoch
T2moc2/3KB (from equating rest-mass energy w/
mean energy of photon - the higher the
temperature the more massive particles can be
produced) Temperature continued to fall with
particles of less less mass dominating Universe
now a soup of electrons, photons, neutrinos,
positrons -particle interactions now occurring
which change balance of protons/neutrons in the
universe - protons start to dominate At t1s
T1010K - density low enough that neutrinos
stopped interacting streamed freely across the
universe At t14 s T 5x109K, most leptons
annihilated, but left enough electrons to balance
the protons
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NUCLEOSYNTHESIS ERA -when most of the H, He a
bit of Li were made
1z3.8x108 T7x108K kT6x104 eV
T180s

• i.e. 3 minutes after big bang
• Universe has cooled down to 1 billion K
• Filled with
• Photons (i.e. parcels of electromagnetic
  radiation)
• Protons (p)
• Neutrons (n)
• Electrons (e)
• also Neutrinos

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NUCLEOSYNTHESIS ERA
1z3.8x108 T7x108K kT6x104 eV
T180s
Before Photons Electrons Protons (1H)
Neutrons Neutrinos After Photons
Nucleons (i.e 1H, 2H, 4He, 7Li)
Neutrinos

• Approximate time when the Planck distribution
  describing distribution of photon energies
  allows deuterium nucleus (2H) to survive.
• Big Bang Nucleosynthesis (BBN) begins.
• This continues for a few hundred sec until most
  of the neutrons are contained within helium-4
  nuclei (4He2) (though some are in 2H, 3He2,
  7Li3etc)
• After this time (BB many hundred s) mean
  particle energies have dropped such that
  "building" of heavier nuclei (beyond 7Li3) is no
  longer efficient. BBN stops.

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Big Bang Nucleosynthesis
The three main "pillars" of evidence in support
of Big Bang cosmology are The Expansion of the
Universe The Cosmic Microwave Background (CMB)
The Abundances of the "Light" Elements We
have now discussed the first two, here we discuss
the third.
By "light" elements, here we are primarily
interested in 1H or p (Hydrogen) 2H
(Deuterium) "fragile" 3H (Tritium) unstable
3He ("Helium-3") "fragile" 4He (Helium)
7Li (Lithium) "fragile"
Note I am being rather "sloppy" in these notes.
Obviously at the time of BBN, all these nuclei
are fully stripped of electrons. Thus I should
really be using 2H (known as a deutron) 4He
etc etc Don't be confused by my sloppiness...
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BBN
How did observed abundances of elements
arise? Not until the 1940s was it was realized H
He were by far the most abundant elements in
the universe - led to significant progress
understanding nuclear reactions (WW II)
Given our understanding of stellar
nucleosynthesis evolution, and given the age of
the universe, it is not possible for stars (of
any type) to have produced as much 4He as we see
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BBN
How did observed abundances of elements arise?
In the Big Bang ...? In 1948, Ralph Alpher
(Hans Bethe) George Gamow suggested that the
during the early stages of the Big Bang, the
densities temperatures might also be sufficient
to allow such thermonuclear reactions
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revisit the past
BB 10-4 s
At temperature 1012 K, the universe a mixture
of photons, electrons (e-), positrons (e)
neutrinos, anti-neutrinos small fraction of
neutrons (n) protons (p) in thermal
equilibrium. Mean thermal energy of the
particles is kT 86 MeV Difference in rest mass
between a proton neutron is mp - mnc2 1.3
MeV Thus neutrons (n) can be converted to
protons (p) and vice versa mediated by electron
neutrinos and antineutrinos The ratio of the
number density of neutrons to protons is simply
given by the Boltzmann equation nn / np EXP(
- mp - mnc2 /kT ) i.e. for T 1012 K,
nn / np 0.985 However, due to the intense
radiation field, and (hence) e-, e density,
fluid only contains 5 protons 5 neutrons for
every 2x1010 photons
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protons neutrons
BB 2 s
Due to expansion, temperature had fallen to
1010 K. Reduced the mean energy of the photons
below 1.02 MeV Pair production ceased existing
e- e pairs were not replaced when they
annihilated, thus proton-to-neutron
neutron-to-proton reactions were no longer
possible. Ratio of the number density of
neutrons to protons at this instant is simply
given by the Boltzmann equation again for T
1010 K, nn / np 0.223 protons dominate
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BB 2-90 s Neutron Decay
Once temperature has fallen to lt 1010 K
neutrons can no longer be created, but these
(free) neutrons can decay Thus ratio of the
numbers of neutrons to protons slowly decreases.
However until the temperature falls below 109
K, the photon density the mean particle
energies are still too high for the products of
nucleosythesis to survive.
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BB 90 s Big Bang Nucleosynthesis (BBN) - 4He
Production
T dropped to 109 K allowing protons neutrons
to combine, producing heavier nuclei. The
primary reaction is of course the production of
deuterium (2H) p n converted to 2H photon
Can then build up the "mass-3" elements tritium
(3H) "Helium-3" (3He) 2H n converted to 3H
photon 2H p converted to 3He photon 2H
2H converted to 3H p 2H 2H converted to
3He n 3He n converted to 3H p And
thus (the relatively stable) "Helium-4" 3He
n converted to 4He photon 3He 2H
converted to 4He p 3H p converted to 4He
photon 3H 2H converted to 4He n
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BB 700s The End of BBN
Rates of reactions depend on baryon density
temperature (now fallen to 108 K) These are
falling as universe expands. BBN has effectively
stopped Relative abundances produced in BBN
can be used to measure baryon density then (and
hence now) BBN makes specific predictions for
2H/1H ratio 3He/1H ratio 4He/1H ratio 7Li/1H
ratio -can be compared to observations Note -
though the 7Li/1H ratio is very small (10-10),
it serves as an important diagnostic since its
prodution is a complex function of baryon
density.
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Baryon Density
Consistent results are obtained for a baryon
density that corresponds to a current baryon
density ?b 2 - 5x10-31 g cm-3 Comparing
this with the critical density ?c 1.1x10-29 g
cm-3 (for H0 75 km/s/Mpc) indicates that
baryonic matter constitutes between 2 and 5
of the material needed to close the universe.
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BB 5x1010 s (1.6x103yr)
1z1.7x104 T3x104K kT2.4 eV
Radiation-Matter Equality
The time when the energy densities of matter
radiation are equal. we made a crude estimate
as to when the energy density in baryons equaled
that in photons. There is disagreement between
that value for z and that above simply because in
the above we have taken into account our current
estimates for the amount of non-baryonic dark
matter in the universe.
Contents Before After Photons Electrons
Nucleons (i.e 1H, 2H, 4He, 7Li)
Neutrinos
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BB 9x1012 s (2.8x105yr)
1z1100 T3x103K kT0.3 eV
Recombination
Contents Before Photons Electrons
Nucleons (i.e 1H, 2H, 4He, 7Li)
Neutrinos After Photons (leading to CMB)
Atoms (ie. 1H, 2H, 4He, 7Li) Neutrinos
The age when the radiation density had fallen
sufficiently that electrons were able to become
bound ( stay bound) to protons.
NOTE Don't be distracted by the re used in the
term "recombination". Protons and electrons were
NEVER previous combined in the early universe.
The term is used simple because the process is
identical to that which occurs is other
astrophysical situations (when the re is
appropriate).
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BB 9x1012 s (2.8x105yr)
1z1100 T3x103K kT0.3 eV
Recombination
Contents Before Photons Electrons
Nucleons (i.e 1H, 2H, 4He, 7Li)
Neutrinos After Photons (leading to CMB)
Atoms (ie. 1H, 2H, 4He, 7Li) Neutrinos
Photons no longer interact sufficiently with
bound electrons, thus the universe becomes
"transparent" to radiation. The binding energy
for an electron in the ground-state of hydrogen
is 13.6 eV. Thus recombination does not occur
until the temperature has fallen sufficiently
such that kT ltlt 13.6 eV. The temperature at
which this occurs is T 3x103K, when the scale
factor was a factor R/R0 1/(1z) 9x10-4 of
its current size.
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